Finite Group DatabasebetaFinite Group DatabasebetaOrder 800.
144 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #87853 | C2 | semidirect |
| 3. C5×#704 | C2 | semidirect |
| 4. #87828 | C2 | semidirect |
| 5. D5×#170 | C2 | semidirect |
| 13. #6032 | C22 | semidirect |
| 14. C5×#170 | C22 | semidirect |
| 29. #704 | D5 | direct (N × H) |
| 38. C5×D5 | M16 | semidirect |
| 55. #170 | C2×D5 | semidirect |
| 59. C52 | C2×M16 | semidirect |
| 93. D5 | #704 | direct (N × H) |
| 104. C5 | D5×M16 | semidirect |
| 105. C5 | C2×#704 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×Dic5 | 2 |
| #87853 | 2 |
| C5×#704 | 2 |
| #87828 | 2 |
| D5×#170 | 2 |
| C2×#704 | 5 |
| D5×M16 | 5 |